Problem: What do the following two equations represent? $x-3y = -3$ $-x+3y = -1$
Solution: Putting the first equation in $y = mx + b$ form gives: $x-3y = -3$ $-3y = -x-3$ $y = \dfrac{1}{3}x + 1$ Putting the second equation in $y = mx + b$ form gives: $-x+3y = -1$ $3y = x-1$ $y = \dfrac{1}{3}x - \dfrac{1}{3}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.